| Formal argumentation theory is a cross-disciplinary topic involving multiple subjects such as mathematics,philosophy,computer science.The argumentation framework(AF)plays a central role in the field of formal argumentation.In the study of AF,the natural language argumentation situation is first modeled as an abstract argumentation system by logical languages,and then the reasoning is executed in the system.At present,AF theory has become a hot research topic in the field of artificial intelligence.Mathematics is a basic tool for the research of AF,such as graph theory,topology,algebra,probability,mathematical logic,etc.When considering the AFs with numerical values,such as fuzzy argumentation framework(FAF),triangular norms and uncertainty theory are the basic research tools.This thesis establishes the labelling-based semantics of FAFs based on fuzzy sets and triangular norms.In recent years,in order to model and reason the natural language argumentation situation more accurately,uncertainty theory has been widely applied in AFs,such as probability,weight,and fuzzy set.The application of uncertainty theory enriches the expressive power of AF in expressing uncertain knowledge.Those AFs involving fuzziness are called fuzzy argumentation frameworks,where arguments and attack relation are associated with fuzzy degree to represent belief degree.The further work is to evaluate the reasonable belief degree of arguments.In the research of Dung's AF,the labelling theory has been widely used to evaluate the acceptability of arguments,establish new semantics,and design efficient algorithms for semantics.Unlike the extension-based semantics(the set of reasonable arguments under specific criteria),which only evaluate the acceptability of arguments,the labelling-based semantics provide more detailed information for arguments,including acceptability,rejection,and undecidability.However,as a common argument-evaluation method,the labelling theory is relatively neglected in various uncertainty AFs.Therefore,this thesis takes the FAF as the basic argumentation system and uses triangular norm as the tool to establish the fuzzy labelling semantics of FAFs.This thesis consists of five chapters.Chapter 1 introduces the purpose and the method of this thesis.And it briefly introduces the history of argumentation framework theory.By analyzing the existing work,this chapter points out the significance of labelling semantics for the evaluation of fuzzy-argument-acceptance.Chapter 2introduces some preliminaries,including triangular norms,fuzzy set theory,argumentation framework,and fuzzy argumentation framework.Chapter 3 introduces fuzzy labelling into FAFs.Then,the fuzzy labelling is applied to represent the accepted degree,rejected degree,and undecided degree of each argument.Next,based on the triangular norms theory,we establish the fuzzy labelling semantics of FAFs by fuzzy labelling,including conflict-free,admissible,complete,preferred,grounded,stable semantics.And there are some newly defined semantics that have not been introduced in FAFs,such as JV-admissible,VJ-admissible,ideal,semi-stable semantics.Chapter 4 describes the relationship between the fuzzy labelling semantics and the extension semantics in FAFs,and the relationship between the labelling semantics in Dung's AFs and the fuzzy labelling semantics in FAFs.Chapter 5summarizes this thesis and remarks the future work.The contributions of this thesis are as follows.First of all,the fuzzy labelling theory in this thesis provides another way for expressing the argumentation semantics of FAFs.It provides a more accurate evaluation method for argumentacceptance and makes some semantics more intuitive.Secondly,fuzzy labelling theory only uses triangular norms to verify whether various semantic criteria are satisfied,which makes the semantics solution easier.Finally,this work also provides some implications for the labelling-based semantics of other quantitative AFs,such as weighted AFs,probabilistic AFs,etc. |
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